Trimmed mean mndlks bezoekers ad VS

*Unverified author*

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Wed, 21 Oct 2009 10:17:33 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142014ewzukqqxmyecyhg.htm/, Retrieved Wed, 21 Oct 2009 18:20:16 +0200

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142014ewzukqqxmyecyhg.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP1W52

Dataseries X:

» Textbox « » Textfile « » CSV «

2357402 2199181 2603060 2629720 2638792 2717481 3810804 3871664 2998364 2923432 2712359 2996099 2395029 2483862 3120231 3360606 3177203 3062783 4242509 4026394 3192481 3118695 2782482 3209833 2630190 2592882 3785309 3231539 3421369 3312134 4647303 4289177 3463853 3304422 3006121 3464238 2921118 2624018 3500718 3939351 3467672 3343628 4852445 4597807 3653145 3572079 3334861 3695369 3075704 2852998 3942704 4004560 3822145 3760085 5267816 5271333 4144142 4109749 3896808 4211074 3402318 3279817 4706628 4079499 4344530 4048625 5394915 5611967 4145481 4025610 3552218 3910443

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 3557533.09722222 89456.144175473 39.7684600651234 Geometric Mean 3480484.75860473 Harmonic Mean 3406034.53921403 Quadratic Mean 3636511.00104404 Winsorized Mean ( 1 / 24 ) 3556716 88079.2890006273 40.3808436734164 Winsorized Mean ( 2 / 24 ) 3554328.36111111 86898.484611399 40.9020753009180 Winsorized Mean ( 3 / 24 ) 3557883.19444444 86184.9521664119 41.2819535778663 Winsorized Mean ( 4 / 24 ) 3540863.69444444 79204.2735957601 44.7054626435459 Winsorized Mean ( 5 / 24 ) 3531444.31944444 76811.2600581897 45.9756071801079 Winsorized Mean ( 6 / 24 ) 3528247.06944444 75466.1607153793 46.7527039403956 Winsorized Mean ( 7 / 24 ) 3523989.31944444 74380.6039476667 47.3777992166329 Winsorized Mean ( 8 / 24 ) 3495899.65277778 69059.3174804662 50.6216942234712 Winsorized Mean ( 9 / 24 ) 3490055.77777778 67694.9732600789 51.5556120299989 Winsorized Mean ( 10 / 24 ) 3493791.75 64856.3299728352 53.8697109667377 Winsorized Mean ( 11 / 24 ) 3489771.70833333 63951.4217559406 54.5691028051172 Winsorized Mean ( 12 / 24 ) 3489673.04166667 60431.7708807982 57.7456690546112 Winsorized Mean ( 13 / 24 ) 3502163.33333333 58346.8214247032 60.0232068828786 Winsorized Mean ( 14 / 24 ) 3508721.36111111 55286.021187135 63.464891952246 Winsorized Mean ( 15 / 24 ) 3502901.36111111 54259.4854307433 64.5583225366597 Winsorized Mean ( 16 / 24 ) 3512188.69444444 50866.1294089993 69.0476892040278 Winsorized Mean ( 17 / 24 ) 3507474.5 50016.189647752 70.1267834415621 Winsorized Mean ( 18 / 24 ) 3509217.75 49710.304581973 70.5933664963417 Winsorized Mean ( 19 / 24 ) 3518615.36111111 46805.3984479128 75.1754173191536 Winsorized Mean ( 20 / 24 ) 3505022.30555556 43846.0835158517 79.9392334389086 Winsorized Mean ( 21 / 24 ) 3516583.38888889 42006.3960656042 83.7154271315446 Winsorized Mean ( 22 / 24 ) 3508219.72222222 40702.6604304279 86.191410711807 Winsorized Mean ( 23 / 24 ) 3522063.48611111 37698.6901773423 93.4266805966629 Winsorized Mean ( 24 / 24 ) 3518774.81944444 35876.9556898155 98.078968847497 Trimmed Mean ( 1 / 24 ) 3547589.07142857 84925.416933013 41.7729956418915 Trimmed Mean ( 2 / 24 ) 3537925.26470588 81146.3465889732 43.5993167089379 Trimmed Mean ( 3 / 24 ) 3528978.12121212 77375.104652033 45.6087023995954 Trimmed Mean ( 4 / 24 ) 3518138.71875 73125.5271527854 48.1109518896096 Trimmed Mean ( 5 / 24 ) 3511541.14516129 70731.828087152 49.6458417677903 Trimmed Mean ( 6 / 24 ) 3506764.38333333 68614.9788486001 51.107854905429 Trimmed Mean ( 7 / 24 ) 3502319.68965517 66420.8085720409 52.7292540538182 Trimmed Mean ( 8 / 24 ) 3498339.55357143 64017.9285252213 54.6462472960708 Trimmed Mean ( 9 / 24 ) 3498746.20370370 62425.4084115456 56.0468292115588 Trimmed Mean ( 10 / 24 ) 3500083.19230769 60753.8839075326 57.6108549312636 Trimmed Mean ( 11 / 24 ) 3500989.16 59305.0802551629 59.0335456075066 Trimmed Mean ( 12 / 24 ) 3502518.8125 57653.0452592991 60.7516705621905 Trimmed Mean ( 13 / 24 ) 3504194.34782609 56323.2405711357 62.2157800632995 Trimmed Mean ( 14 / 24 ) 3504450 55046.9904018779 63.6628810115738 Trimmed Mean ( 15 / 24 ) 3503926.97619048 54027.1860700901 64.8548856800499 Trimmed Mean ( 16 / 24 ) 3504050.05 52855.3362624494 66.2951046721354 Trimmed Mean ( 17 / 24 ) 3503086.26315789 52011.73141831 67.3518486624477 Trimmed Mean ( 18 / 24 ) 3502570 50981.9020413671 68.7022229409563 Trimmed Mean ( 19 / 24 ) 3501787.91176471 49551.2951542552 70.6699572809045 Trimmed Mean ( 20 / 24 ) 3499795.1875 48248.0262390973 72.5375825770873 Trimmed Mean ( 21 / 24 ) 3499167.93333333 47139.0179887604 74.2308194491379 Trimmed Mean ( 22 / 24 ) 3497035.42857143 45926.2058684873 76.1446621257027 Trimmed Mean ( 23 / 24 ) 3495627.61538462 44404.2385282194 78.722836631082 Trimmed Mean ( 24 / 24 ) 3492179.45833333 42965.3417782227 81.278987057968 Median 3464045.5 Midrange 3905574 Midmean - Weighted Average at Xnp 3488942.81081081 Midmean - Weighted Average at X(n+1)p 3502570 Midmean - Empirical Distribution Function 3488942.81081081 Midmean - Empirical Distribution Function - Averaging 3502570 Midmean - Empirical Distribution Function - Interpolation 3502570 Midmean - Closest Observation 3488942.81081081 Midmean - True Basic - Statistics Graphics Toolkit 3502570 Midmean - MS Excel (old versions) 3503086.26315789 Number of observations 72

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142014ewzukqqxmyecyhg/1plik1256141851.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142014ewzukqqxmyecyhg/1plik1256141851.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142014ewzukqqxmyecyhg/26tgm1256141851.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t1256142014ewzukqqxmyecyhg/26tgm1256141851.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

geomean <- function(x) { return(exp(mean(log(x)))) } harmean <- function(x) { return(1/mean(1/x)) } quamean <- function(x) { return(sqrt(mean(x*x))) } winmean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) win <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn } return(win) } trimean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) tri <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { tri[j,1] <- mean(x,trim=j/n) tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2) } return(tri) } midrange <- function(x) { return((max(x)+min(x))/2) } q1 <- function(data,n,p,i,f) { np <- n*p; i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q2 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q3 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- data[i+1] } } q4 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- (data[i]+data[i+1])/2 } else { qvalue <- data[i+1] } } q5 <- function(data,n,p,i,f) { np <- (n-1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i+1] } else { qvalue <- data[i+1] + f*(data[i+2]-data[i+1]) } } q6 <- function(data,n,p,i,f) { np <- n*p+0.5 i <<- floor(np) f <<- np - i qvalue <- data[i] } q7 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- f*data[i] + (1-f)*data[i+1] } } q8 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { if (f == 0.5) { qvalue <- (data[i]+data[i+1])/2 } else { if (f < 0.5) { qvalue <- data[i] } else { qvalue <- data[i+1] } } } } midmean <- function(x,def) { x <-sort(x[!is.na(x)]) n<-length(x) if (def==1) { qvalue1 <- q1(x,n,0.25,i,f) qvalue3 <- q1(x,n,0.75,i,f) } if (def==2) { qvalue1 <- q2(x,n,0.25,i,f) qvalue3 <- q2(x,n,0.75,i,f) } if (def==3) { qvalue1 <- q3(x,n,0.25,i,f) qvalue3 <- q3(x,n,0.75,i,f) } if (def==4) { qvalue1 <- q4(x,n,0.25,i,f) qvalue3 <- q4(x,n,0.75,i,f) } if (def==5) { qvalue1 <- q5(x,n,0.25,i,f) qvalue3 <- q5(x,n,0.75,i,f) } if (def==6) { qvalue1 <- q6(x,n,0.25,i,f) qvalue3 <- q6(x,n,0.75,i,f) } if (def==7) { qvalue1 <- q7(x,n,0.25,i,f) qvalue3 <- q7(x,n,0.75,i,f) } if (def==8) { qvalue1 <- q8(x,n,0.25,i,f) qvalue3 <- q8(x,n,0.75,i,f) } midm <- 0 myn <- 0 roundno4 <- round(n/4) round3no4 <- round(3*n/4) for (i in 1:n) { if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){ midm = midm + x[i] myn = myn + 1 } } midm = midm / myn return(midm) } (arm <- mean(x)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') lb <- win[,1] - 2*win[,2] ub <- win[,1] + 2*win[,2] if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() bitmap(file='test2.png') lb <- tri[,1] - 2*tri[,2] ub <- tri[,1] + 2*tri[,2] if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Measure',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.element(a,'S.E.',header=TRUE) a<-table.element(a,'Value/S.E.',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE) a<-table.element(a,arm) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean')) a<-table.element(a,armose) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE) a<-table.element(a,geo) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE) a<-table.element(a,har) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE) a<-table.element(a,qua) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) for (j in 1:length(win[,1])) { a<-table.row.start(a) mylabel <- paste('Winsorized Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(win[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE) a<-table.element(a,win[j,1]) a<-table.element(a,win[j,2]) a<-table.element(a,win[j,1]/win[j,2]) a<-table.row.end(a) } for (j in 1:length(tri[,1])) { a<-table.row.start(a) mylabel <- paste('Trimmed Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(tri[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE) a<-table.element(a,tri[j,1]) a<-table.element(a,tri[j,2]) a<-table.element(a,tri[j,1]/tri[j,2]) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE) a<-table.element(a,median(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE) a<-table.element(a,midr) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[1]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[2]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[3]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[4]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[5]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[6]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[7]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[8]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Number of observations',header=TRUE) a<-table.element(a,length(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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